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In this paper, a geometric function is introduced to reflect the attenuationspeed of impact of one firm's default to its partner. If two firms arecompetitions (copartners), the default intensity of one firm will decrease(increase) abruptly when the other firm defaults. As time goes on, the impactwill decrease gradually until extinct. In this model, the joint distributionand marginal distributions of default times are derived by employing the changeof measure, so can we value the fair swap premium of a CDS.

A Model for Counterparty Risk with Geometric Attenuation Effect and the Valuation of CDS